Sr Examen
Integral de (cos(x))^3/(4*(sin(x)^2)-1) dx
Solución
Ha introducido
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1 / | | 3 | cos (x) | ------------- dx | 2 | 4*sin (x) - 1 | / 0
$$\int\limits_{0}^{1} \frac{\cos^{3}{\left(x \right)}}{4 \sin^{2}{\left(x \right)} - 1}\, dx$$
Integral(cos(x)^3/(4*sin(x)^2 - 1), (x, 0, 1))
Respuesta (Indefinida)
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/ | /x\ / 2/x\ /x\\ / 2/x\ /x\\ 2/x\ / 2/x\ /x\\ 2/x\ / 2/x\ /x\\ | 3 8*tan|-| 3*log|1 + tan |-| + 4*tan|-|| 3*log|1 + tan |-| - 4*tan|-|| 3*tan |-|*log|1 + tan |-| + 4*tan|-|| 3*tan |-|*log|1 + tan |-| - 4*tan|-|| | cos (x) \2/ \ \2/ \2// \ \2/ \2// \2/ \ \2/ \2// \2/ \ \2/ \2// | ------------- dx = C - --------------- - ----------------------------- + ----------------------------- - ------------------------------------- + ------------------------------------- | 2 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ | 4*sin (x) - 1 16 + 16*tan |-| 16 + 16*tan |-| 16 + 16*tan |-| 16 + 16*tan |-| 16 + 16*tan |-| | \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{\cos^{3}{\left(x \right)}}{4 \sin^{2}{\left(x \right)} - 1}\, dx = C + \frac{3 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{16 \tan^{2}{\left(\frac{x}{2} \right)} + 16} + \frac{3 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} - 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{16 \tan^{2}{\left(\frac{x}{2} \right)} + 16} - \frac{3 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{2} \right)}}{16 \tan^{2}{\left(\frac{x}{2} \right)} + 16} - \frac{3 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 4 \tan{\left(\frac{x}{2} \right)} + 1 \right)}}{16 \tan^{2}{\left(\frac{x}{2} \right)} + 16} - \frac{8 \tan{\left(\frac{x}{2} \right)}}{16 \tan^{2}{\left(\frac{x}{2} \right)} + 16}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.